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Many practical systems in physics, biology, engineering and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. The problems of finite-time stability analysis are investigated for a class of Markovian switching stochastic systems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop systems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffusion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities (LMls). A numerical example is presented to illustrate the proposed methodology.